Properties of atoms in electronically excited molecules within the formalism of TDDFT.

The topological analysis of the electron density for electronic excited states under the formalism of the quantum theory of atoms in molecules using time-dependent density functional theory (TDDFT) is presented. Relaxed electron densities for electronic excited states are computed by solving a Z-vector equation which is obtained by means of the Sternheimer interchange method. This is in contrast to previous work in which the electron density for excited states is obtained using DFT instead of TDDFT, that is, through the imposition of molecular occupancies in accordance with the electron configuration of the excited state under consideration. Once the electron density of the excited state is computed, its topological characterization and the properties of the atoms in molecules are obtained in the same manner that for the ground state. The analysis of the low-lying π→π* singlet and triplet vertical excitations of CO and C6H6 are used as representative examples of the application of this methodology. Altogether, it is shown how this procedure provides insights on the changes of the electron density following photoexcitation and it is our hope that it will be useful in the study of different photophysical and photochemical processes.